13-Hendrix diamond

The 13-Hendrix diamond is the tonality diamond generated from the ratios 1/1, 13/12, 5/4, 3/2 and 13/8.

	1/1	13/12	5/4	3/2	13/8
	24/13	1/1	15/13	18/13	3/2
	8/5	26/15	1/1	6/5	13/10
	4/3	13/9	5/3	1/1	13/12
	16/13	4/3	20/13	24/13	1/1

All notes in the Hendrix diamond are also found in the 15-limit tonality diamond, because 1/1:13/12:5/4:3/2:13/8 is a 15-limit anomalous saturated suspension.

Symmetry group

The symmetry group of the 13-Hendrix diamond has 16 elements. Its generators are:

• 3:2, 5:4, 13:8 → 13:12, 5:3, 13:9
• 3:2, 5:4, 13:8 → 3:2, 15:13, 18:13
• 3:2, 5:4, 13:8 → 4:3, 8:5, 16:13

Orbits and Invariant Subsets

[to be included]